1. Field of the Invention
The present invention relates to an optical deflector and an optical apparatus, such as an image forming apparatus and a display, using the optical deflector. The optical deflector is suitably used in, e.g., a projection display for projecting an image with a deflection scan of light and an image forming apparatus which includes an electrophotographic process, such as a laser beam printer and a digital copying machine.
2. Description of the Related Art
Hitherto, optical deflectors have been proposed in various forms of optical scanning systems or optical scanning apparatuses for sinusoidally vibrating a moving element, which has a reflecting surface, to deflect a light. The optical scanning system using the optical deflector, which causes sinusoidal vibrations utilizing a resonance phenomenon, has different features in comparison with the optical scanning system using a rotating mirror such as a rotatable polygon mirror. For example, the optical scanning systems, the size of the optical deflector can be reduced and power consumption is small. Further, an optical deflector made of a single Si crystal, which is manufactured by a semiconductor process, is theoretically free from metal fatigue and has durability.
For optical deflectors utilizing the resonance phenomenon, there is known a technique for simultaneously exciting two or more natural oscillation modes in the torsional vibrating direction and causing an optical scan other than the sinusoidal optical scan. More specifically, an optical deflector is proposed in U.S. Pat. No. 4,859,846 (hereinafter “Patent Document 1”), in which two or more natural oscillation modes are simultaneously excited about the same axis, to thereby perform a triangular scan at an essentially constant angular speed. FIG. 13 is a block diagram for explaining the optical deflector, disclosed in Patent Document 1, in which two natural oscillation modes are simultaneously excited to perform a triangular scan at an essentially constant angular speed.
The disclosed optical deflector 1012 comprises a first moving element (mass) 1014, a second moving element (mass) 1016, a first torsion spring 1018 for resiliently coupling and supporting the first and second moving elements, and a second torsion spring 1020 for supporting the second moving element 1016 and a mechanical ground surface 1023. Those components are all caused to torsionally vibrate about a torsion axis 1026 by a driver 1030. The first moving element 1014 has a reflecting surface to deflect a light. Thus, a light from a light source is deflected to make a scan by the torsional vibrations of the first moving element 1014. For the torsional vibrations about the torsion axis 1026, the optical deflector 1012 has a primary natural oscillation mode at a fundamental frequency and a secondary natural oscillation mode at nearly third harmonic frequency triple the fundamental frequency. The driver 1030 drives the optical deflector 1012 at two frequencies, i.e., the frequency of the primary natural oscillation mode and the frequency of the secondary natural oscillation mode, which is in phase with the former frequency and is triple. In other words, the optical deflector 1012 causes the torsional vibrations not only in the primary natural oscillation mode, but also in the secondary natural oscillation mode at the same time. Accordingly, a displacement angle in the deflection scan of the light reflected by the first moving element 1014 is given by superimposition of the two vibration modes and is changed following a nearly triangular waveform instead of a sine waveform. As a result, an angular speed of the deflection scan is held essentially constant over a wider region than the case where the displacement angle is changed following the sine waveform, and, thus, a practically available region can be increased with respect to the overall region of the deflection scan.
On the other hand, a meander structure is known as a small-sized spring structure manufactured by the semiconductor process. See Barillaro et al,., “Analysis, simulation and relative performances of two kinds of serpentine springs”, Journal of Micromechanics and Microengineering, 15(2005) PP736-746 (hereinafter “Non-Patent Document 1”). FIGS. 12A-12C show one example of the meander structure described in Non-Patent Document 1. FIG. 12A is a plan view, FIG. 12B illustrates a similar structure portion repeated, and FIG. 12C is a perspective sectional view taken along a section plane XIIC-XIIC in FIG. 12A, looking in the direction of an arrow. As shown in FIG. 12A, a meander spring 93 is formed to extend from a movable end 90 to a fixed end 91 in the illustrated shape. The meander spring 93 has a rectangular cross-section with a width of W and a thickness of H, as shown in FIG. 12C.
Considering contributions to a torsion spring constant Kθ, as shown in FIG. 12B, the meander spring 93 can be approximated by a structure that flexible springs with a length J and a torsion spring with a length T are coupled to each other in series. Thus, in the illustrated spring structure, a plurality of flexible springs and a plurality of torsion springs are coupled to each other essentially in series between the movable end 90 and the fixed end 91. Therefore, the torsion spring constant Kθ can be reduced with respect to a torsional displacement about an oscillation axis 17 with the repetition of the similar structure portion. Such a point can be theoretically understood from studies taking into account the number of the repeated similar structure portions, the transverse elastic coefficient of the spring material, and the longitudinal elastic coefficient of the spring material.
When a condition of J<<T is satisfied, this essentially means a structure in which the torsion springs each having the length T and a torsion axis 23 parallel to the oscillation axis 17 are coupled to each other. In such a case, the torsion spring constant Kθ can also be reduced by increasing the number of the torsion springs without increasing a total length. Further, as understood from the above-suggested theoretical studies, since the torsion spring constant Kθ is substantially in linear proportion to the thickness H, a relatively low spring constant can be obtained even when the thickness H is large. On the other hand, the torsion spring constant Kθ is substantially in proportion to the third power of the width W.
There is known an example of applying the above-described feature to a spring structure used in the semiconductor manufacturing process in which it is difficult to select the thickness of the spring material as a free design parameter (e.g., a spring structure in an optical deflector). See Kudrle et al., “Single-crystal silicon micromirror array with polysilicon flexures”, Sensor and Actuators, A119(2005) PP559-566.
In the vibration systems having a plurality of oscillatory moving elements and a plurality of torsion springs, unless the frequencies of the natural oscillation modes as driving targets are adjusted to desired values, the relationship among those frequencies affects the oscillatory vibration of the oscillatory moving element which deflects and scans a light, thus degrading not only the scanning frequency, but also the scanning waveform.
However, when the above-described known vibration systems are reduced in size, non-linearity of the torsion spring is noticeable. Such a drawback has impeded a size reduction of the optical deflector because of a difficulty in inspecting and adjusting the frequencies of the natural oscillation modes as the driving targets.